In some time-reversal communication systems, when a transceiver A intends to transmit information to a transceiver B, transceiver B first sends a delta-like pilot pulse that propagates through a scattering and multi-path environment, and the signals are received by transceiver A. Transceiver A transmits time-reversed signals back through the same channel to transceiver B. Based on channel reciprocity, a time-reversal communication system leverages the multi-path channel as a matched filter, i.e., treats the environment as a facilitating matched filter computing machine, and focuses the wave at the receiver in both space and time domains.